Ignoramus21381 wrote:
Thanks to all. Yes, obviously, the lids would breathe. The question
is, would desiccant be able to take care of relatively little moisture
that enters the boxes during said "breathing".

If the parts are just sitting open in the bins, no way. The
dessicant would be saturated in a week or less. If you could
put the stuff in zip-lock bags and get everything in the bins
without the sharp edges poking tiny holes in the bags, then it
might work.
That stuff is kind of valuable on a per tool basis. I placed moisture
measuring pieces of paper that came with desiccant, in the boxes, I
will see how they change.

OK, then at least you will know how long it stays dry, but it
won't be very long unless the covers are pretty tight. The
advantage of the bags is they can expand and crumple inwards in
response to thermal expansion and atmospheric pressure changes
without actually exchanging any air inside to outside.
Spraying them all with oil, is not very practicable.
I use LPS1. They used to sell it in an economical pump sprayer
bottle that did a good job of atomizing the stuff. They don't
have that bottle available anymore, but you can buy it in
aerosol cans or buy the bulk container and provide your own
sprayer. It is kind of like WD-40 but I think it is much better
-- more lube and less evaporation. It doesn't make everything
gooey, and you can just wipe it off most things. It is good for
removing cosmolene-type stuff, too.

Jon